CN113297531B - Method for solving direct current power flow equation under perfect phase estimation - Google Patents

Method for solving direct current power flow equation under perfect phase estimation Download PDF

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CN113297531B
CN113297531B CN202110430057.5A CN202110430057A CN113297531B CN 113297531 B CN113297531 B CN 113297531B CN 202110430057 A CN202110430057 A CN 202110430057A CN 113297531 B CN113297531 B CN 113297531B
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高放
吴国键
郭苏杭
杨铭宇
殷林飞
代伟
双丰
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    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract

The invention provides a method for solving a direct current power flow equation under perfect phase estimation. The invention saves the consumption of quantum bit resources in the process of solving the direct current flow equation in an iteration mode, can solve a large-scale direct current flow equation based on a small-scale quantum system under the condition of perfect phase estimation, avoids the problem that the direct current flow equation cannot be solved by utilizing a quantum program due to insufficient quantum bit resources, and provides the method for solving the direct current flow equation based on the existing hardware platform with quantum bit resource limitation.

Description

Method for solving direct current power flow equation under perfect phase estimation
Technical Field
The invention belongs to the field of power systems, and relates to a method for solving a direct current power flow equation under perfect phase estimation.
Background
The power flow calculation of the power system is the most basic calculation and the most important calculation of the power system. The load flow calculation is to know the wiring mode, parameters and operation conditions of the power grid and calculate the voltage of each bus, the current and power of each branch and the network loss when the power system operates in a steady state. The direct current power flow model is a linear model formed by simplifying a nonlinear model in power flow calculation, so that the calculation becomes simple, and the direct current power flow model has great advantages in some scenes such as overload check calculation and the like which have low requirements on solving precision.
Eskandarpour et al, at Denver university, in the text Quantum Computing Solution of DC Power Flow, after linearization of the Flow equation, use Harrow, Hassdim and the HHL algorithm proposed in 2009 by Lloyd to achieve calculation acceleration and perform simple example demonstration, which can reduce the time complexity for solving the linear equation set to O (log (N) s 2 κ 2 Epsilon), an exponential level of acceleration is achieved compared to the current best classical algorithm.
The HHL algorithm stores the obtained solution of the direct current power flow equation in the quantum register, extracts information which is actually normalized through measurement, and needs to obtain a normalization constant in a back substitution mode if the actual solution is obtained, so that the algorithm capable of directly obtaining the non-normalized solution is developed, and the method has remarkable significance.
Meanwhile, the number of required quantum bits in the HHL algorithm is increased along with the increase of the scale of the direct current power flow equation, the large-scale practical application of the HHL algorithm is established on the premise of the existing general quantum computer, and the large-scale practical application of the HHL algorithm is currently in the noisy intermediate quantum era, the quantum bit resources are limited (the number is 50-100, and quantum noise exists at the same time), so that the method for developing the direct current power flow equation with less required quantum bit number has important practical significance and application prospect on the premise.
And then
Figure BDA0003031038330000011
In an iterative phase estimation algorithm provided in the article of the iterative access critical phase estimation and estimation algorithm using a single angular aperture qubit, the phase estimation precision is improved by increasing iteration times instead of bit number, so that the rigorous requirement on the number of quantum bits can be reduced (only one auxiliary quantum bit is used at least).
Disclosure of Invention
The technical problem to be solved by the invention is that the existing quantum algorithm for solving the direct current power flow equation needs to occupy a large amount of quantum bit resources, so that the method for solving the direct current power flow equation based on perfect iterative phase estimation is provided. The direct current power flow equation is that P is active power, B is a susceptance matrix, and θ is a phase angle to be solved. When the characteristic value of B can be completely coded by a finite-digit binary number, namely the phase can be perfectly estimated, the solution theta of the direct-current power flow equation is obtained by measuring the state of the quantum system in the iteration process and extracting and processing information.
The invention adopts the following technical scheme for solving the technical problems:
1. a method for solving a direct current power flow equation under perfect phase estimation is characterized in that the method is a classical-quantum hybrid algorithm based on perfect iterative phase estimation, the solution of the direct current power flow equation is obtained by processing a measurement result of a quantum circuit of the perfect iterative phase estimation through a classical computer, and the method mainly comprises the following steps:
(1) an iterative phase estimation route is designed according to the scale of a quantum system and is divided into a single auxiliary quantum bit route, an N auxiliary quantum bit route and any auxiliary quantum bit route;
(2) extracting the characteristic value lambda of the susceptance matrix B in the direct current power flow equation j And the projection | beta of the phase angle theta on each eigenvector of the susceptance matrix B j |；
(3) Extracting absolute value of each element of characteristic vector of susceptance matrix B j |；
(4) By carrying out beta j u j Sign calibration;
(5) lambda extracted according to steps (2) and (4) j And beta j u j By passing
Figure BDA0003031038330000021
And calculating to obtain a solution of the direct current power flow equation.
2. The method for solving the direct current power flow equation under the perfect phase estimation is characterized in that in the step (2), lambda is j And | β j Extracting | and counting the information stored in the classical register after the last iteration is finished, wherein the classical register stores lambda j Has a probability of
Figure BDA0003031038330000023
Extraction of lambda j And | β j |。
3. The method for solving the direct current power flow equation under the perfect phase estimation is characterized in that | u in the step (3) j Extracting | by performing post-selection operation on the system state, and when the measurement result of m rounds of iteration is lambda j Then, the measurement is executed to the bottom register, the information stored in the classical register is counted, and | u is extracted j |。
4. The method for solving the direct current power flow equation under the perfect phase estimation is characterized in that in the step (4), beta is j u j The sign calibration of | β extracted by the step (2) of claim 1 j And | u extracted in step (3) j L and equation
Figure BDA0003031038330000022
Calibrating beta j u j Sign information of (a).
Drawings
Fig. 1 is a diagram of a quantum wire based on a single-assisted qubit mixing algorithm.
Fig. 2 is a quantum wire diagram based on an N-assisted qubit mixing algorithm.
Fig. 3 is a diagram of a quantum wire based on an arbitrary assisted qubit mixing algorithm.
Detailed Description
The invention designs three iterative phase estimation routes according to the quantum system scale. When qubit resources are scarce, as shown in embodiment one, an iterative phase estimation route based on single auxiliary qubits is designed; when the number of allocable qubits of the top register is greater than N, as shown in embodiment two, an iterative phase estimation route based on N auxiliary qubits is designed; and the third embodiment provides an iterative phase estimation route based on any auxiliary qubits, so that the method has higher flexibility.
1. The first embodiment. Referring to fig. 1, fig. 1 is a quantum circuit diagram based on a single-auxiliary qubit hybrid algorithm, and a process of solving a dc power flow equation is as follows:
(1) as shown in fig. 1, a first iteration is performed, after which the quantum register is initialized, wherein
Figure BDA0003031038330000031
Where B, i.e., the dc power flow equation P, is equal to the susceptance matrix B in B θ, the same applies below. In this round of iteration, the rotation parameter ω of the Rz gate m ＝-2π(0.0) 2 Wherein (0.0) 2 Representing a binary decimal number of 0.0, as follows. The case that the measurement result in the first iteration is 0 is recorded as C m_0 And the case where the measurement result is 1 is denoted as C m_1 And m represents the mth bit of the characteristic value of the susceptance matrix from left to right. C is to be m_0 The probability of occurrence is denoted as P m_0 ，C m_1 The probability of occurrence is denoted as P m_1 ；
(2) And executing a second iteration, and initializing the quantum register after iteration. In the round of iteration, the rotation parameters of the Rz gate in the round of iteration are designed according to the following three cases: case one, P m_0 ＝1，P m_1 When the value is equal to 0, the value is (m-1) ＝-2π(0.00) 2 Designing a rotation parameter for the next iteration; case two, P m_0 ＝0，P m_1 1, mixing ω with (m-1) ＝-2π(0.01) 2 Designing a rotation parameter for the next iteration; case three, P m_1 ≠0，P m_1 Not equal to 0, labeled here and the current experiment noted as experiment 1. Design the rotation parameter ω for the next iteration in experiment 1 (m-1) ＝-2π(0.00) 2 And designing a rotation parameter omega in the second iteration of experiment 2 (m-1) ＝-2π(0.01) 2 . Let C denote the case where the measurement results of the first and second iterations are 00 (m-1)m_00 And its corresponding probability is denoted as P (m-1)m_00 . Recording N eigenvalues lambda of N-dimensional susceptance matrix j ＝φ j ＝0.φ j1 φ j2 …φ jm After the second iteration, obtain
Figure BDA0003031038330000032
And
Figure BDA0003031038330000033
(3) through m rounds of iteration, information is extracted from the classical register
Figure BDA0003031038330000034
And their corresponding probabilities
Figure BDA0003031038330000035
To this end, information λ is extracted from the measurement results j And | β j |；
(4) The measurement result at m iterations is λ j ＝φ j ＝(0.φ j1 φ j2 …φ j(m-1) φ jm ) 2 Then, the bottom register is measured to extract the characteristic vector u of the susceptance matrix B j Absolute value of each element j |；
(5) According to the equation
Figure BDA0003031038330000036
The following equations are associated:
Figure BDA0003031038330000041
due to | beta j u j |＝|β j |×|u j If the specific numerical value is known, the positive sign of the coefficient is verified by traversal to obtain beta j u j Sign information of (a).
(6) Extracting the information lambda j ，β j u j By passing
Figure BDA0003031038330000042
And (5) performing operation to solve the direct current power flow equation.
2. The second embodiment. Referring to fig. 2, fig. 2 is a quantum circuit diagram based on N-assisted qubit mixing algorithm, in which the top register contains N qubits anc _ q [0] to anc _ q [ N-1], and the flow of solving the dc power flow equation is as follows:
(1) as shown in fig. 2, a first iteration is performed. In this iteration, only one auxiliary qubit in the top register is used, with the rotation parameter set to ω m_0 ＝-2π(0.0) 2 Extracting information C m_0 ，C m_1 ，P m_0 And P m_1 ；
(2) The quantum wire graph and rotation parameters for the second iteration are designed according to the following three cases: case one, P m_0 ＝1，P m_1 At 0, in the second iteration, only anc _ q [0] is used in the top register]One qubit with rotation parameter designed as ω (m-1)_0 ＝-2π(0.00) 2 This was used as anc _ q [0]]Rotation parameters of the upper Rz gate; case two, P m_0 ＝0，P m_1 In the second iteration, only anc _ q [0] is used in the top register, 1]One qubit with rotation parameter designed to be omega (m-1)_0 ＝-2π(0.01) 2 This was used as anc _ q [0]]Rotation parameters of the upper Rz gate; case three, P m_1 ≠0，P m_1 Not equal to 0, secondIn round iterations, anc _ q [0] is used in the top register]And anc _ q [ 1]]Two quantum bits, and rotation parameter is designed to be omega (m-1)_0 ＝-2π(0.00) 2 And ω (m-1)_1 ＝-2π(0.01) 2 Will be ω (m-1)_0 As anc _ q [0]]Rotation parameter of upper Rz Gate, will ω (m-1)_1 As anc _ q [ 1] in the second iteration]Rotation parameters of the upper Rz gate. Through the iteration, the information P is extracted (m-1)m_00 ，P (m-1)m_10 ，P (m-1)m_01 And P (m-1)m_11 。
(3) By analogy, as shown in FIG. 2, assume that the divergence of the first measurement results occurs at the x-th measurement 1 Round iteration, then anc _ q [ 1] will be performed in the next round of iteration]Put into use, assume that the divergence of the N-1 st measurement results occurs at the x-th N-1 Round iteration, then x N-1 After a round of iterations, the N qubits in the top register are put into use. After m iterations, information lambda is extracted j ＝φ j ＝0.φ j1 φ j2 …φ j(m-1) φ jm And its corresponding probability
Figure BDA0003031038330000043
Then get | beta j |。
(4) The | u given in step (4) in example I is used j Scheme for extracting | u | j |；
(5) Beta given in step (5) of example I was used j u j Sign calibration scheme, extracting beta j u j Integral information;
(6) and (4) solving the direct current power flow equation by adopting the solution scheme given in the step (6) in the first embodiment.
3. Example three. Referring to fig. 3, fig. 3 is a quantum circuit diagram based on any auxiliary qubit mixture algorithm, in which the top register contains n qubits anc _ q [0] to anc _ q [ n-1], and the flow of solving the dc power flow equation is as follows:
(1) in the first iteration, traversing is performed on a scheme with possible rotation parameters, and the setting of each experimental rotation parameter is shown in the following table;
Figure BDA0003031038330000051
complete 2 of the first iteration n After 1 experiment, information was extracted excluding the results with probability zero
Figure BDA0003031038330000052
(2) In the second iteration, let ω -2 π (n) bin ) 2 Wherein n is bin Is a binary decimal with a different phi j(m-n+1) φ j(m-n+2) …φ jm Is n bin Setting rotation parameters from the n items from right to left and from the n +1 item from right to left according to the ergodic thought in the first iteration; when m can be divided by n, all characteristic value information lambda is extracted through m/n iterations j ＝φ j ＝0.φ j1 φ j2 …φ j(m-1) φ jm And
Figure BDA0003031038330000053
after evolution, | beta is obtained j |。
(3) The | u given in step (4) in example I is used j Scheme for extracting | u | j |；
(4) Beta given in step (5) of example I was used j u j Sign calibration scheme for extracting beta j u j Integral information;
(5) and (4) solving the direct current power flow equation by adopting the solution scheme given in the step (6) in the first embodiment.

Claims (1)

1. A method for solving a direct current power flow equation under perfect phase estimation is characterized in that the method is a classical-quantum hybrid algorithm based on perfect iterative phase estimation, and the solution of the direct current power flow equation is obtained by processing a measurement result of a quantum circuit of the perfect iterative phase estimation through a classical computer; the direct current power flow equation is P ═ B theta; wherein P is active power; b is a susceptance matrix; theta is the phase angle to be solved; providing an iterative phase estimation line designed according to the scale of the quantum system; when the quantum bit resource is deficient, an iterative phase estimation circuit based on single auxiliary quantum bit is designed; when the number of the quantum bits distributed by the top register is larger than N, designing an iterative phase estimation circuit based on N auxiliary quantum bits; the iterative phase estimation circuit based on any auxiliary qubit and having higher flexibility solves the direct current power flow equation by the following process:
(1) extracting the characteristic value lambda of the susceptance matrix B in the direct current power flow equation j And the projection | beta of the phase angle theta on each eigenvector of the susceptance matrix B j L: through iteration, information is extracted from the classical register
Figure FDA0003750570480000011
And their corresponding probabilities
Figure FDA0003750570480000012
To this end, information λ is extracted from the measurement results j And | β j |；
(2) Extracting absolute value of each element of characteristic vector of susceptance matrix B j L: the measurement result at m iterations is λ j ＝φ j ＝(0.φ j1 φ j2 …φ j(m-1) φ jm ) 2 Then, the bottom register is measured to extract the characteristic vector u of the susceptance matrix B j Absolute value of each element j |；
(3) By carrying out beta j u j And (3) sign calibration: according to the equation
Figure FDA0003750570480000013
Simultaneous system of equations due to | β j u j |＝|β j |×|u j If the specific numerical value is known, the positive sign of the coefficient is verified by traversal to obtain beta j u j Sign information of (a);
(4) extracting the information lambda j ，β j u j By passing
Figure FDA0003750570480000014
And (5) performing operation to solve the direct current power flow equation.
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